https://file.aiquickdraw.com/mathbot/file/1726701980327d60i88o1.jpg

Let's solve each composite function using the given tables of ordered pairs.

### 19) \((f \circ g)(36)\)

This represents \( f(g(36)) \).
1. First, find \( g(36) \) from the table: \( g(36) = 6 \).
2. Now, find \( f(6) \) from the table: \( f(6) = 21 \).

Thus, \((f \circ g)(36) = 21\).

### 20) \((g \circ g)(16)\)

This represents \( g(g(16)) \).
1. First, find \( g(16) \) from the table: \( g(16) = 4 \).
2. Now, find \( g(4) \) from the table: \( g(4) = 2 \).

Thus, \((g \circ g)(16) = 2\).

### 21) \((g \circ f)(4)\)

This represents \( g(f(4)) \).
1. First, find \( f(4) \) from the table: \( f(4) = 1 \).
2. Now, find \( g(1) \) from the table: \( g(1) = 1 \).

Thus, \((g \circ f)(4) = 1\).

### 22) \((f \circ f)(4)\)

This represents \( f(f(4)) \).
1. First, find \( f(4) \) from the table: \( f(4) = 1 \).
2. Now, find \( f(1) \) from the table: \( f(1) = -14 \).

Thus, \((f \circ f)(4) = -14\).

---

Would you like more details on how composite functions work, or explanations on other concepts? Here are five follow-up questions:

1. What is the general formula for composite functions?
2. Can you explain the difference between \(f \circ g\) and \(g \circ f\)?
3. How do you know if a function is composite or not?
4. How does squaring affect the values of a function like \(f(x) = x^2 - 15\)?
5. What would happen if we input a negative number into \(g(x) = \sqrt{x}\)?

**Tip:** When solving composite functions, always evaluate from the innermost function outward!

Learn how to solve composite functions using function tables for f(x) = x^2 - 15 and g(x) = √x. This guide walks through examples like (f ∘ g)(36), (g ∘ g)(16), and more, breaking down the steps for Grades 9-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation